Average Error: 1.6 → 0.2
Time: 3.7s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.8540150644513744 \cdot 10^{56} \lor \neg \left(x \le 3.6071842534283706 \cdot 10^{-82}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.8540150644513744 \cdot 10^{56} \lor \neg \left(x \le 3.6071842534283706 \cdot 10^{-82}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

\end{array}
double f(double x, double y, double z) {
        double r33348 = x;
        double r33349 = 4.0;
        double r33350 = r33348 + r33349;
        double r33351 = y;
        double r33352 = r33350 / r33351;
        double r33353 = r33348 / r33351;
        double r33354 = z;
        double r33355 = r33353 * r33354;
        double r33356 = r33352 - r33355;
        double r33357 = fabs(r33356);
        return r33357;
}
↓
double f(double x, double y, double z) {
        double r33358 = x;
        double r33359 = -6.854015064451374e+56;
        bool r33360 = r33358 <= r33359;
        double r33361 = 3.6071842534283706e-82;
        bool r33362 = r33358 <= r33361;
        double r33363 = !r33362;
        bool r33364 = r33360 || r33363;
        double r33365 = 4.0;
        double r33366 = r33358 + r33365;
        double r33367 = y;
        double r33368 = r33366 / r33367;
        double r33369 = z;
        double r33370 = r33369 / r33367;
        double r33371 = r33358 * r33370;
        double r33372 = r33368 - r33371;
        double r33373 = fabs(r33372);
        double r33374 = r33358 * r33369;
        double r33375 = r33366 - r33374;
        double r33376 = r33375 / r33367;
        double r33377 = fabs(r33376);
        double r33378 = r33364 ? r33373 : r33377;
        return r33378;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -6.854015064451374e+56 or 3.6071842534283706e-82 < x

    1. Initial program 0.4

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    2. Using strategy rm

    3. Applied div-inv0.4

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]

    4. Applied associate-*l*0.3

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]

    5. Simplified0.3

      \[\leadsto \left|\frac{x + 4}{y} - x \cdot \color{blue}{\frac{z}{y}}\right|\]

    if -6.854015064451374e+56 < x < 3.6071842534283706e-82

    1. Initial program 2.5

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    2. Using strategy rm

    3. Applied associate-*l/0.2

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]

    4. Applied sub-div0.2

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.8540150644513744 \cdot 10^{56} \lor \neg \left(x \le 3.6071842534283706 \cdot 10^{-82}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))